A Hydraulic Optimal Section of Cubic Parabolic Open Water Conveying Channel and Its Solution Method
A parabola-shaped, optimal cross-section technology, which is applied in data processing applications, predictions, instruments, etc., can solve the problems of complex calculation of cross-section wetted circumference and inconvenient engineering practice
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example 1
[0242] Example 1 (Approximate Solution of Wet Perimeter)
[0243] Two cubic parabolic channel sections, shape coefficient a = 0.5, water depth h = 1.5m, calculate the wetted circumference.
[0244] First use formula (3) to get
[0245] Using the method of numerical integration, the theoretical value of the wet perimeter is obtained Integral method is generally obtained with the help of computer programs, which is not suitable for engineering practice. Using the approximate formula provided by the present invention The error is only 0.0057m. When h = 1.0 ~ 2.5m, use the approximate method and the integral method to calculate the wet area respectively, and the results are shown in Table 3.
[0246] Table 3 Comparison table of wetted area calculated by approximation method and integral method
[0247] Water depth h(m) Integral method (m) Approximate formula method (m) Absolute error (m) 0.5 2.365065570 2.364690946 0.000375 1.0 3.493780872 3.4...
example 2
[0249] Example 2 (known flow, design channel section)
[0250] There is a channel, known Q=10m3 / s,S o =1 / 15000, n=0.014s / m 1 / 3 . Now it is necessary to design a channel, which requires the minimum flow area and wetted area under a certain flow capacity, or the maximum flow capacity under a certain area.
[0251] According to cubic parabolic section design: Substituting the known data into formula (31), formula (32) ~ formula (34) and formula (25), it can be obtained that h = 2.91m, B = 6.14m, A = 13.39m 2 , P=9.25m, a=0.100.
[0252] According to quadratic parabola design: substituting the known data into formula (37), formula (35) and formula (38) ~ formula (40), it can be obtained that h=3.13m, a=0.302, B=6.45m, A= 13.49m 2 , P=9.41m.
[0253] Design according to other cross-sectional shapes: the same method can be used to calculate the design dimensions of semi-cubic parabola, trapezoidal cross-section and catenary cross-section, as shown in Table 4.
[0254] It can...
example 3
[0258] Example 3 (comparison of flow capacity and construction cost)
[0259] A water delivery channel with a total length of 100Km. Q=12m 3 / s,n=0.014s / m 1 / 3 ,S o =1 / 20000, f=0.5m. Unit canal length, lining cost C l = 50 yuan / m 2 , earthwork excavation cost C e 30 yuan / m 2 , land acquisition fee C a = 15 yuan / m. The local hydrogeological conditions are good, and the slope coefficient is not limited. Now it is necessary to design a hydraulic optimum section and calculate the construction cost.
[0260] Substituting the known data into Table 1, the dimensions of different shapes (cubic parabola, quadratic parabola, semi-cubic parabola, catenary shape, trapezoid) can be obtained, and the results are listed in Table 5. From the comparison results, it can be obtained that the cubic parabolic channel section has the smallest water depth, water surface width, water passing area and wetted area, or in other words, under the same conditions, it has the largest flow capacity...
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